Question of interest: From what population did an individual originate?

Assignment Tests

Uses in fisheries and conservation

a. Allow managers to determine rates of movements among populations

c. Assigning individuals to breeding populations

d. Assigning individuals to hatcheries of origin

Assumptions:

a. Hardy-Weinberg equilibrium (the expected frequency of a genotype can be determine from population allele frequencies

b. loci are independentc. accurate estimation of population allele

frequencies (i.e., large population sample sizes)

Steps in classical assignment methods:a. genotype unknown individual b. calculate population allele frequencies for all

possible populations of originc. calculate the expected frequency of the unknown

individual’s genotype in each possible population of origin

d. multiply these expected frequencies across loci for each population separately (see example)

e. assign unknown to population where its genotype is most likely to occur (highest expected frequency)

Here is an actual example from lake sturgeon sampled from locations in open waters of Lake Michigan

Baseline (river) spawning adult samples Open water samples of unknown origin Long handle dip nets Commercial gill and trap netsCaptured in spring Captured year round

1 cm2 dorsal fin clip, stored dry 1 cm2 dorsal fin clip, stored drySpawning in river

River Mouth Samples Open Water SamplesNear or within river mouths Presumed independent of

spawning population

50 km

Kalamazoo RiverFox River

Manistee RiverMenominee River

Muskegon River

Peshto River

Sampling locations

Lake Michigan

Oconto River

Laboratory Methods

Individual1 2

Step 2 - extract DNA and using polymerase chain reaction (PCR) methods, genotype individuals

PCR

Step 3 – use electrophoresis to resolve genotypes

RR

R

RRR R

RY

Y

YY

YY

YY

Population 1 Population 2

Step 4 - estimate allele frequencies (e.g., frequency of yellow and red alleles in each spawning (baseline) population

Step 1 – capture adults and take asmall fin sample

Student Question – Given a genetic data set of genotype frequencies for each trait (color and letter) for each breeding population (e.g., MI vs WI), what breeding population did fish ‘?’originate from?

? Based on the color and letter(genotypes) assuming color and letter are 2 independent loci,which population did the circled fish originate from

W

M

WW

M

M

M

M M

M

M

M

M

W

W

W

W

W

W

M

M

Probability of origin based on the expectedfrequencies of ‘genotypes at 2 loci in WI and MILocation MWI 1/10 2/10 = 2/100MI 4/10 8/10 = 32/100

Total

Example: two loci where the allele frequencies for alleles ‘R’ and ‘r’ for locus 1 and ‘T’ and ‘t’for locus 2 are estimated for 2 populations (A and B). Unlike to example with color and letters above, for most loci, genotypes are composed of 2 alleles (one inherited from the mother and father). Thus, we must use the Hardy Weinberg principle to estimate the ‘expected’ frequency of genotypes for individuals from each population based on the population allele frequencies that can be estimated by sampling and genotyping fish from each spawning population

Locus 1 Locus 2pop A freq(R) freq(r) freq(T) freq(t)

0.5 0.5 0.4 0.6Pr(RR) Pr(Rr) Pr(rr) Pr(TT) Pr(Tt) Pr(tt)p2 2p(1-p) (1-p)2 p2 2p(1-p) (1-p)2

0.25 0.5 0.25 0.16 0.48 0.36

pop B 0.9 0.1 0.6 0.40.81 0.18 0.01 0.36 0.48 0.16

Unknown genotype: RRTTLikelihood of observing RRTT from pop A:Likelihood of observiing RRTT from pop B:

(0.25)(0.16) = 0.04(0.81)(0.36) = 0.29

HardyWeinbergExpectedfrequency

)ˆ|ypeProb(genot)ˆ|ypeProb(genot

B

A

B

ALL

Assign individual to population A of ratio >1 and to population Bif ratio <1

where A Band are estimates of population allele frequenciesfor populations A and B, respectively

Likelihood estimators for individual assignment

)ˆ|ypeProb(genot)ˆ|ypeProb(genot

B

A

B

ALL

Likelihood estimators for individual assignment

Decision RuleAssign individual to population A if ratio >1 and to population Bif ratio <1

where A Bandare estimates of population allelefrequencies for populationsA and B (e.g., WI and MI), respectivelyfor traits ‘M’ and

Incorporating UncertaintyInto Assignment Decisions

WolfRiver Black

River

Figure describing locations associated with Lesson 10 (population analysis of allele frequencies and assignment testing. The rivers circled are the Wolf and Fox Rivers in Wisconsin and the CheboyganRiver in Michigan.

Scenario – In the 1980’s some young lake sturgeon from the Cheboygan River and from the Wolf River were stocked into Burt Lake in Michigan. Some years later, biologists were conducting surveys in BurtLake and found that a number of fish captured were of a size that were consistent with the fish stocked.The fish were untagged and so visually, biologists were not able to determine whether the fish were fromthe stocked Wisconsin fish or Michigan fish. Biologists requested that a genetic analysis be conducted.

There are several steps to the genetic analysis. First, population allele frequencies have to be estimatedfrom the two rivers (Wolf/Fox and Cheboygan). If the rivers differ in allele frequencies, then an assignmenttest can be used to genotype the fish sampled in Burt Lake to determine origin.